Remove redundant total_ordering decorator usage

src/pymatgen/core/periodic_table.py

@@ -876,7 +876,6 @@ def print_periodic_table(filter_function: Callable | None = None) -> None:
             print(" ".join(row_str))
 
 
-@functools.total_ordering
 class Element(ElementBase):
     """Enum representing an element in the periodic table."""
 
@@ -1597,14 +1596,12 @@ def from_dict(cls, dct: dict) -> Self:
         return cls(dct["element"], dct["oxidation_state"], spin=dct.get("spin"))
 
 
-@functools.total_ordering
 class Specie(Species):
     """This maps the historical grammatically inaccurate Specie to Species
     to maintain backwards compatibility.
     """
 
 
-@functools.total_ordering
 class DummySpecie(DummySpecies):
     """This maps the historical grammatically inaccurate DummySpecie to DummySpecies
     to maintain backwards compatibility.

src/pymatgen/core/structure.py

@@ -6,6 +6,7 @@
 from __future__ import annotations
 
 import collections
+import collections.abc
 import contextlib
 import functools
 import inspect
@@ -1098,22 +1099,24 @@ def __init__(
         self._properties = properties or {}
 
     def __eq__(self, other: object) -> bool:
+        """Define equality by comparing all three attributes: lattice, sites, properties."""
         needed_attrs = ("lattice", "sites", "properties")
 
-        # Return NotImplemented as in https://docs.python.org/3/library/functools.html#functools.total_ordering
         if not all(hasattr(other, attr) for attr in needed_attrs):
             return NotImplemented
 
-        # TODO (DanielYang59): fix below type
-        other = cast(Structure, other)  # make mypy happy
-
         if other is self:
             return True
-        if len(self) != len(other):
+
+        if hasattr(other, "__len__") and len(self) != len(other):
             return False
-        if self.lattice != other.lattice:
+
+        if hasattr(other, "lattice") and self.lattice != other.lattice:
             return False
-        if self.properties != other.properties:
+        if hasattr(other, "properties") and self.properties != other.properties:
+            return False
+
+        if not hasattr(other, "__contains__"):
             return False
         return all(site in other for site in self)